4/4/2019 Correlations

Distinguishing Characteristics of Correlation 4/4/2019 Distinguishing Characteristics of Correlation Correlational procedures involve one sample containing all pairs of X and Y scores Neither variable is called the IV or DV Use the individual pair of scores to create a scatterplot

Correlation Coefficient 4/4/2019 Correlation Coefficient Describes three characteristics of the relationship: Direction Form Degree

What Is A Large Correlation? 4/4/2019 What Is A Large Correlation? Guidelines: 0.00 to <±.30 – low ±.30 to <±.50 – moderate >±.50 – high While 0 means no correlation at all, and 1.00 represents a perfect correlation, we cannot say that .5 is half as strong as a correlation of 1.0

4/4/2019 Pearson Correlation Used to describe the linear relationship between two variables that are both interval or ratio variables The symbol for Pearson’s correlation coefficient is r The underlying principle of r is that it compares how consistently each Y value is paired with each X value in a linear manner

Calculating Pearson r There are 3 main steps to r: 4/4/2019 Calculating Pearson r There are 3 main steps to r: Calculate the Sum of Products (SP) Calculate the Sum of Squares for X (SSX) and the Sum of Squares for Y (SSY) Divide the Sum of Products by the combination of the Sum of Squares

4/4/2019 1) Sum of Products To determine the degree to which X & Y covary (numerator) We want a score that shows all of the deviation X & Y have in common Sum of Products (also known as the Sum of the Cross-products) This score reflects the shared variability between X & Y The degree to which X & Y deviate from the mean together SP = ∑(X – MX)(Y – MY)

Sums of Product Deviations 4/4/2019 Sums of Product Deviations Computational Formula n in this formula refers to the number of pairs of scores

4/4/2019 2) Sum of Squares X & Y For the denominator, we need to take into account the degree to which X & Y vary separately We want to find all the variability that X & Y do not have in common We calculate sum of squares separately (SSX and SSY) Multiply them and take the square root

4/4/2019 2) Sum of Squares X & Y The denominator: =

Hypothesis testing with r 4/4/2019 Hypothesis testing with r Step 1) Set up your hypothesis Step 2) Find your critical r-score Alpha and degrees of freedom

Hypothesis testing with r 4/4/2019 Hypothesis testing with r Step 3) Calculate your r-obtained Step 4) Compare the r-obtained to r-critical, and make a conclusion If r-obtained < r-critical = fail to reject Ho If r-obtained > r-critical = reject Ho

Coefficient Of Determination 4/4/2019 Coefficient Of Determination The squared correlation (r2) measures the proportion of variability in the data that is explained by the relationship between X and Y Coefficient of Non-Determination (1-r2): percentage of variance not accounted for in Y

Correlation in Research Articles 4/4/2019 Correlation in Research Articles Coleman, Casali, & Wampold (2001). Adolescent strategies for coping with cultural diversity. Journal of Counseling and Development, 79, 356-362

Other Types of Correlation 4/4/2019 Other Types of Correlation Spearman’s Rank Correlation variable X is ordinal and variable Y is ordinal Point-biserial correlation variable X is nominal and variable Y is interval Phi-coefficient variable X is nominal and variable Y is also nominal Rank biserial variable X is nominal and variable Y is ordinal